Difference between revisions of "2019 IMO Problems/Problem 3"
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Initially, <math>1010</math> users have <math>1009</math> friends each, and <math>1009</math> users have <math>1010</math> friends each. Prove that there exists a sequence of such events after which each user is friends with at most one other user. | Initially, <math>1010</math> users have <math>1009</math> friends each, and <math>1009</math> users have <math>1010</math> friends each. Prove that there exists a sequence of such events after which each user is friends with at most one other user. | ||
| − | == | + | == Video Solution== |
https://youtu.be/p16MaqdvBQQ | https://youtu.be/p16MaqdvBQQ | ||
Revision as of 01:50, 19 November 2023
Contents
[hide]Problem
A social network has 
users, some pairs of whom are friends. Whenever user 
is friends with user 
, user is also friends with user . Events of the following kind may happen repeatedly, one at a time:
Three users , , and 
such that is friends with both and , but and are not friends, change their friendship statuses such that and are now friends, but is no longer friends with , and no longer friends with . All other friendship statuses are unchanged.
Initially, 
users have 
friends each, and users have friends each. Prove that there exists a sequence of such events after which each user is friends with at most one other user.
Video Solution
Solution
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See Also
| 2019 IMO (Problems) • Resources | ||
| Preceded by Problem 2 |
1 • 2 • 3 • 4 • 5 • 6 | Followed by Problem 4 |
| All IMO Problems and Solutions | ||
